On my screen the core is still showing as thicker lines. The stud layer is anyway. Some of the outer lines on the CMU-mtl stud wall type lose thickness but it appears to be gyp layers only which are thinner on the other wall types.
The question still remains, what is making those dots. It is like there is a small fillet at the corners drawn in a different line style than the rest of the wall componants.
Mike (or anyone), can you explain how you set up your wall types to have the core component different from the rest? I think the answer is in there somewhere, but I can't figure that part out...
OK, since for some reason the forum won't let me edit my previous post, here goes:
The problem is a lack of consistency between your overrides in the Cut Line Styles settings and the Object Style settings. In your Object Styles, you have the Projection lineweight set to 2, but in the Cut Line Styles settings, you have all of the functions (other than Structure ) set to 1. If you change them to 2 here, then the dots go away.
You apparently can't have a discrepancy between the two, since you can't override the Cut Line Styles of just the Structure  components without also affecting the others (Substrate , Thermal/Air Layer , etc.). If you set all the non-structure components to a line weight of 2, then everything shows up as you intend for it to.
Hope that helps (see image below).